Question

You notice that Delta’s "6.5s45" bonds (coupon rate 6.5%) closed at 90.5. (Bond prices are expressed as a percentage of par.) The par value is $1,000. These mature in exactly 25 years (from now would be in 2045). The first coupon is paid six months from now. What is the nominal yield to maturity of these bonds (this is the conventional yield)? The bonds pay coupons semiannually. Answer in percent to three decimal places. Do not enter the percent sign.

Answer 1

Face value of bond = 1000

market price 90.5% = 1000*90.5% = 905

coupon rate = 6.5%

semiannual coupon rate (i) =face value*coupon rate/2

=1000*6.5%/2 =32.5

semiannual years to maturity (n) =25*2 =50

Bond price formula = (C*(1-(1/(1+i)^n))/i) + (face value/(1+i)^n)

905 = 32.5*(1-(1/(1+i)^50))/i)+(1000/(1+i)^50)

i is that rate called yield to maturity semiannual at which bond price is equal to $905

Assume i is 3.5%

bond price =(32.5*(1-(1/(1+3.5%)^50))/3.5%)+(1000/(1+3.5%)^50)

=941.3609553

assume i is 4%

bond price =(32.5*(1-(1/(1+4%)^50))/4%)+(1000/(1+4%)^50)

=838.8836154

Interpolation formula for rate calculation = Lower rate + ((upper rate -lower rate)/(upper value - lower value)*(upper value - actual bond value))

3.5% + ((4%-3.5%)/(941.3609553-838.8836154)*(941.3609553-905))

=0.03677409734

Annual rate or APR =semiannual rate *number of semiannual period in year

=0.03677409734*2

=0.07354819468 or 7.35%

So Nominal yield to maturity of this bond would be 7.35% (answer may differ by +-0.02% due to manual calculations)

Note: excel or financial calculator function = rate(number of periods, payment per period, -present value, future value)*number of semiannual period in year

=rate(50, 32.5, -905, 1000)*2

=7.33%